Specifically for when they mean "a little".
In what situations would they be used and are they completely interchangeable without any differences?
It seems to be a lot about nuances.
You have someone talking about it on this page.
It says that you can replace 少し with ちょっと in most cases but it's less common the other way around. Then it lists few examples when the sentence does not convey exactly the same meaning based on which one you use.
One of the example is from a book and it talks about the difference between 「ちょっと待ってね」 and 「少し待ってね」. The first one would be an egoist way of asking the people to wait, a bit vague, term that would be convenient for you. The other one with 少し would be apparently more accurate, easier to rely on and let the other person more likely to feel at ease/trust with you.
An other example is a case when you cannot really use 少し instead if ちょっと. The example is 「ちょっと、わかんない。」.
I am not sure I fully understand myself but what I understood so far is that 少し, compared to ちょっと, is ちゃんとした言葉 compared to ちょっと that would be a bit 適当 (sorry I don't find the words to explain that in english). This difference would be reflected especially when you ask someone to do something.
To a certain extent they are just different levels of politeness. Check the following:
少々（しょうしょう）> 少し > ちょっと
The phrases get longer the more polite they are. Also, I believe ちょっと is more of a spoken phrase than a written phrase.